Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules.
Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules.
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DOI：
10.1214/09-ss051
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发表时间：
2010
影响因子：
3.3
通讯作者：
Proschan MA
中科院分区：
文献类型：
--
作者：
Fay MP;Proschan MA
在假设检验的数学方法中，我们从一组明确定义的假设开始，并为这些假设选择具有最佳属性的检验。在实践中，我们经常从不太精确的假设开始。例如，研究人员通常想知道两组中哪一组通常具有较大的响应，并且 t 检验或 Wilcoxon-Mann-Whitney (WMW) 检验都可以接受。尽管 t 检验和 WMW 检验通常都与完全不同的假设相关，但任一检验的决策规则和 p 值都可能与许多不同的假设集（我们称之为视角）相关联。将可应用决策规则的许多不同视角集中在一个位置是有用的，因为每个视角都允许对相关 p 值进行不同的解释。这里我们收集了很多这样的观点，用于二样本t检验、WMW检验和其他相关检验。我们讨论每个视角下的有效性和一致性，并根据这些许多不同的视角讨论测试之间的建议。最后，我们简要讨论用于测试遗传中立性的决策规则，其中多种观点的知识对于决策规则的正确解释至关重要。
In a mathematical approach to hypothesis tests, we start with a clearly defined set of hypotheses and choose the test with the best properties for those hypotheses. In practice, we often start with less precise hypotheses. For example, often a researcher wants to know which of two groups generally has the larger responses, and either a t-test or a Wilcoxon-Mann-Whitney (WMW) test could be acceptable. Although both t-tests and WMW tests are usually associated with quite different hypotheses, the decision rule and p-value from either test could be associated with many different sets of assumptions, which we call perspectives. It is useful to have many of the different perspectives to which a decision rule may be applied collected in one place, since each perspective allows a different interpretation of the associated p-value. Here we collect many such perspectives for the two-sample t-test, the WMW test and other related tests. We discuss validity and consistency under each perspective and discuss recommendations between the tests in light of these many different perspectives. Finally, we briefly discuss a decision rule for testing genetic neutrality where knowledge of the many perspectives is vital to the proper interpretation of the decision rule.